Ali, I am just seeing the comment because I have been away from MO for a while. So you are saying that even an ill-founded ultrapower by a non-normal filter as long as it is weakly amenable can be used to show that kappa is weakly compact in M?

Let's make some additional assumptions on the ultrafilter $U$. Suppose $M\models{\rm ZFC}^-$ and $\kappa$ is a cardinal in $M$. We say that $U$ is an $M$-ultrafilter if $\langle M,\in,U\rangle$ satisfies that $U$ is a $\kappa$-complete normal ultrafilter on $\kappa$. Because $U$ is only $\kappa$-complete for sequences in $M$ and $M$ might be missing even countable […]

← Older revision Revision as of 11:23, 15 March 2018 Line 3: Line 3: For those interested, there is a discord server created by me and [[User:Zetapology|Zetapology]]: https://discord.gg/tbGrU39 For those interested, there is a discord server created by me and [[User:Zetapology|Zetapology]]: https://discord.gg/tbGrU39 −My "ideal background theory" (or just "prefered theory") is $\text{ZFC + GCH + […]